Xunan Tunich means stone woman in Maya, and this is how the local people refer to the site. However, in the reports of old travelers it is generally called Benque Viejo.

"This ceremonial centre is an outlying member of, and on the eastern fringe of, a dense
concentration of Maya sites in the eastern part of the Peten district of Guatemala
which includes such well-known major sites as Tikal, Uaxactun and Naranjo. After examining the Maya remains in the whole of the Belize river valley, G.R.Willey and others suggested that Xunantunich may in fact have been a fairly important provincial centre, perhaps a regional capital.

Whether this capital of the "Belize valley community" itself owed allegiance to the much larger sites further west is a matter for conjecture. Certainly the fine astronomical carved frieze on the main palace building at Xunantunich should indicate that the priests there were in the main stream of Maya intellectual culture."

E. Mackie, New Light on the End of Classic Maya Culture at Benque Viejo, British Honduras, p. 8.